L ECTURE 3 Notes are modified from EvoNet Flying Circus slides. Found at: ceick/ai/EC1.ppt.

LECTURE 3

Notes are modified from EvoNet Flying Circus slides.

Found at: www2.cs.uh.edu/~ceick/ai/EC1.ppt

OUTCOMES

At the end you should be able to discuss: Basics of evolutionary computation Representation At least two selection approaches What crossover is. What is the link between genetic programming

and genetic algorithms.

THE STEPS

In order to build an evolutionary algorithm there are a number of steps that we have to perform:

1. Design a representation2. Decide how to initialize a population3. Design a way of mapping a genotype to a

phenotype4. Design a way of evaluating an individual

FURTHER STEPS

5. Design suitable mutation operator(s)6. Design suitable recombination operator(s)7. Decide how to manage our population8. Decide how to select individuals to be

parents9. Decide how to select individuals to be

replaced10. Decide when to stop the algorithm

DESIGNING A REPRESENTATION

Come up with a method of representing an individual solution.

Must be relevant to the problem that we are solving.

Bear in mind how the solutions will be evaluated and what the genetic operators might be.

EXAMPLE: DISCRETE REPRESENTATION (BINARY ALPHABET)

CHROMOSOMECHROMOSOME

GENEGENE

Representation of an individual can be using discrete values (binary, integer, etc.). Following is an example of binary representation.

EXAMPLE: DISCRETE REPRESENTATION (BINARY ALPHABET)

8 bits Genotype

Phenotype:• Integer

• Real Number

• Schedule

• ...

• Anything?

EXAMPLE: DISCRETE REPRESENTATION (BINARY ALPHABET)

Phenotype could be integer numbers

Genotype:

1*21*27 7 + 0*2+ 0*26 6 + 1*2+ 1*25 5 + 0*2+ 0*24 4 + 0*2+ 0*23 3 + 0*2+ 0*22 2 + 1*2+ 1*21 1 + 1*2+ 1*200 ==

128 + 32 + 2 + 1 = 163128 + 32 + 2 + 1 = 163

= 163Phenotype:

EXAMPLE: DISCRETE REPRESENTATION (BINARY ALPHABET)

Phenotype could be a Schedulee.g. 8 jobs, 2 time steps

Genotype:

=

12345678

21211122

JobTime Step

Phenotype

EXAMPLE: REAL-VALUED REPRESENTATION

A very natural encoding if the solution we are looking for is a list of real-valued numbers, then encode it as a list of real-valued numbers!

Lots of applications, e.g. parameter optimisation

Personal example: Work on evolutionary algorithms and evoked potentials.

EXAMPLE: ORDER BASED REPRESENTATION

Individuals are represented as permutations Used for ordering/sequencing problems Famous example: Travelling Salesman

Problem where every city gets a assigned a unique number from 1 to n. A solution could be (5, 4, 2, 1, 3).

Needs special operators to make sure the individuals stay valid permutations.

Example: Tree-based representation

Individuals in the population are trees. Approach leads to Genetic Programming These functions and terminals can be anything:

Functions: sine, cosine, add, sub, and, If-Then-Else, Turn...

Terminals: X, Y, 0.456, true, false, , Sensor0… Example: calculating the area of a circle:

2* r

* *

r r

EVALUATING AN INDIVIDUAL

This is by far the most costly step for real applicationsdo not re-evaluate unmodified individuals

It might be a subroutine, a black-box simulator, or any external process(e.g. robot experiment)

MUTATION OPERATORS

We might have one or more mutation operators for our representation. Some important points are:

At least one mutation operator should allow every part of the search space/pattern space to be reached

The size of mutation is important and should be controllable.

Mutation should produce valid chromosomes (i.e. valid possible solutions)

EXAMPLE: MUTATION FOR DISCRETE REPRESENTATION

1 1 1 1 1 1 1 before

1 1 1 0 1 1 1 after

Mutation usually happens with a certain probability for each gene

mutated gene

EXAMPLE: MUTATION FOR REAL VALUED REPRESENTATION

Adding some random noise

Often, a Gaussian/normal distribution N(0,) is used, where

• 0 is the mean value

• is the standard deviation

and

x’i = xi + N(0,i)

for each parameter

EXAMPLE: MUTATION FOR ORDER BASED REPRESENTATION (SWAP)

7 83 41 2 6 5

7 83 46 2 1 5

Randomly select two different genes and swap them.

Example: Mutation for tree based representation

*

2 *

r r

*

*

r r

Single point mutation selects one node and replaces it with a similar one.

RECOMBINATION OPERATORS

We might have one or more recombination operators for our representation. Some important points are: The child should inherit something from each

parent. The recombination operator should be designed in

conjunction with the representation. Recombination should produce valid chromosomes

EXAMPLE: RECOMBINATION FOR DISCRETE REPRESENTATION

Whole Population: . . .

Each chromosome is cut into n pieces which are recombined. (Example for n=1)

1 1 1 1 1 1 1 0 0 0 0 0 0 0 parentscut cut

1 1 1 0 0 0 0 0 0 0 1 1 1 1 offspring

EXAMPLE: RECOMBINATION FOR ORDER BASED REPRESENTATION (ORDER1)

Choose an arbitrary part from the first parent and copy this to the first child

Copy the remaining genes that are not in the copied part to the first child:

• starting right from the cut point of the copied part

• using the order of genes from the second parent

• wrapping around at the end of the chromosome

Repeat this process with the parent roles reversed

EXAMPLE: RECOMBINATION FOR ORDER BASED REPRESENTATION (ORDER1)

7 83 41 2 6 5 78 16 5234

81 2

7, 3, 4, 6, 5

4, 3, 6, 7, 5

order

7 85 41 2 3 6

Parent 1 Parent 2

Child 1

SELECTION STRATEGY

We want to have some way to ensure that better individuals have a better chance of being parents than less good individuals.This will give us selection pressure which will drive the population forward.We have to be careful to give less good individuals at least some chance of being parents - they may include some useful genetic material.

EXAMPLE: ROULETTE WHEEL

BestWorst

Better (fitter) individuals have:

more space more chances to be

selected

EXAMPLE: TOURNAMENT SELECTION

Select k random individuals, without replacement

Take the best k is called the size of the tournament

REPLACEMENT STRATEGY

The selection pressure is also affected by the way in which we decide which members of the population to kill in order to make way for our new individuals.

ELITISM

Should fitness constantly improve? Re-introduce in the population previous best-so-far

(elitism) or Keep best-so-far in a safe place (preservation)

RECOMBINATION VS MUTATION

Recombination modifications depend on the whole population decreasing effects with convergence exploitation operator

Mutation mandatory to escape local optima strong causality principle exploration operator

STOPPING CRITERION

The optimum is reached!

Limit on CPU resources:

Maximum number of fitness

evaluations

Limit on the user’s patience:

After some generations without improvement

PRACTICAL PERFORMANCE

Never draw any conclusion from a single run use statistical measures (averages, medians) from a sufficient number of independent runs

ALGORITHM PERFORMANCE (2)

Remember the WYTIWYG principal:

“What you test is what you get” - don´t tune algorithm performance on toy data and expect it to work with real data.

KEY ISSUES

What you say are the six key points you should leave this session with?

Please discuss it groups.